Assignment:
Q1. X is a finite random variable whose p.m.f. is given below.
x 1 2 3
fx(X) 0.4 0.2 0.4
(i) Compute the mean, μx, of X.
(ii) Compute the variance, V(x), of X.
(iii) Compute the standard deviation, x. of X.
Q2. The following sample of size n= 4 was taken for the values of a random variable, X.
7,4,4,9
(i) Compute the sample mean, x bar.
(ii) Compute the sample standard deviation, s.
Q3. Let T be the random variable that gives the time, in hours, for a rush order of parts to arrive at your business. The parameters for T are μ subscript T = 12 and T = 3. Let t bar be the random variable that is the mean of a random sample of n = 100 delivery times.
(i) μ t
(ii) t
(iii) Give a formula for the random variable, S, that is the standardization of t bar.
(iv) What is the approximate distribution of S?
Provide complete and step by step solution for the question and show calculations and use formulas.